c
(c) \(\uparrow: N+F \sin \theta=W \Rightarrow N=W-F \sin \theta\)

The block will move if

\(F \cos \theta \geq f_{\max }\)

\(F \cos \theta \geq \mu(W-F \sin \theta)\)

\(\mu=\tan \alpha=\frac{\sin \alpha}{\cos \alpha}\)

\(F \cos \theta \geq \frac{\sin \alpha}{\cos \alpha}(W-F \sin \theta)\)

\(F(\cos \theta \cos \alpha+\sin \theta \sin \alpha) \geq W \sin \alpha\)

\(F \geq \frac{W \sin \alpha}{\cos (\theta-\alpha)}\)

\(F_{\min }=\frac{W \sin \alpha}{\cos (\theta-\alpha)}\)